When the lions were unveiled, some claimed that they were too sedate, not regal and ferocious enough. (More epithets in this 2011 New York Times article.) Mayor Fiorello LaGuardia named them Patience and Fortitude - qualities he felt felt New Yorkers would need to survive the Great Depression of the 1930s.
For years the lions were decorated with holly wreaths, top hats, and even Mets and Yankees caps; but on the advice of conservators, the practice has been discontinued.
Potter got the commission for the lions at the recommendation of Augustus Saint-Gaudens. The carving was the work of the Piccirilli brothers (see the Maine Monument, the Firemen's Memorial, and more).
The New York Public Library's site has more info.
New York Public's attic sculpture, MacMonnies sculptures, flagpole bases ... I'll get to them one of these days.